Wormhole paper

Can someone help me understand exactly what a0 is in the following paper (page9)?http://arxiv.org/pdf/1405.1283v1.pdf
"where a0 ≡ be−∆/2 (60) is a fixed length that can only be determined by experiment."

Found it in this article which has a better diagram:
http://www.kicc.cam.ac.uk/news/wormholes-negative-energy [Broken]

The author gives the interpretation of it just below your equation. I haven't read the paper, but in normalizations where you encounter logs the argument of the log should be dimensionless. In particle physics this often means introducing a certain mass scale, here it means introducing a length-scale (which is the inverse thing, basically) which turns out to be the throat radius for which the Casimir energy vanishes.

Maybe it helps to compare it with Zee's QFT in a Nutshell, chapter 1.8 about the Casimir effect; there, a length scale d appears, being the distance between the plates.